Symmetry restoration and the gluon mass in the Landau gauge

We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.

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BRST analysis and BFV quantization of the generalized quantum rigid rotor

Modern Physics Letters A ◽

10.1142/s0217732321501169 ◽

2021 ◽

pp. 2150116

Author(s):

Ronaldo Thibes

Keyword(s):

Field Theory ◽

Sigma Model ◽

Brst Symmetry ◽

Symmetry Analysis ◽

Nonlinear Sigma Model ◽

Canonical Structure ◽

Rigid Rotor ◽

Gauge Invariant ◽

Gauge Fixing ◽

Functional Quantization

We identify a strong similarity among several distinct originally second-class systems, including both mechanical and field theory models, which can be naturally described in a gauge-invariant way. The canonical structure of such related systems is encoded into a gauge-invariant generalization of the quantum rigid rotor. We perform the BRST symmetry analysis and the BFV functional quantization for the mentioned gauge-invariant version of the generalized quantum rigid rotor. We obtain different equivalent effective actions according to specific gauge-fixing choices, showing explicitly their BRST symmetries. We apply and exemplify the ideas discussed to two particular models, namely, motion along an elliptical path and the [Formula: see text] nonlinear sigma model, showing that our results reproduce and connect previously unrelated known gauge-invariant systems.

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Massive gravity from double copy

Journal of High Energy Physics ◽

10.1007/jhep12(2020)030 ◽

2020 ◽

Vol 2020 (12) ◽

Cited By ~ 1

Author(s):

Arshia Momeni ◽

Justinas Rumbutis ◽

Andrew J. Tolley

Keyword(s):

Sigma Model ◽

Massive Gravity ◽

Effective Field ◽

Effective Theory ◽

Nonlinear Sigma Model ◽

Limit Theory ◽

Four Dimensions ◽

Yang Mills ◽

Massive Spin ◽

Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

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On gauge independence for gauge models with soft breaking of BRST symmetry

International Journal of Modern Physics A ◽

10.1142/s0217751x1450184x ◽

2014 ◽

Vol 29 (30) ◽

pp. 1450184 ◽

Cited By ~ 10

Author(s):

Alexander Reshetnyak

Keyword(s):

Gauge Theories ◽

Brst Symmetry ◽

Landau Gauge ◽

Functional Integral ◽

Yang Mills ◽

Gauge Models ◽

S Matrix ◽

Gauge Fixing ◽

Dependent Parameter ◽

Quantum Treatment

A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field–antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang–Mills and gravity theories. The Gribov–Zwanziger action and the refined Gribov–Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.

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NON-RENORMALIZABILITY OF THE MASSIVE N = 2 SUPER-YANG–MILLS THEORY

Modern Physics Letters A ◽

10.1142/s0217732391002335 ◽

1991 ◽

Vol 06 (23) ◽

pp. 2143-2154 ◽

Cited By ~ 8

Author(s):

G. A. KHELASHVILI ◽

V. I. OGIEVETSKY

Keyword(s):

Perturbation Theory ◽

Fourth Order ◽

Sigma Model ◽

Nonlinear Sigma Model ◽

Harmonic Superspace ◽

Yang Mills ◽

Super Yang Mills Theory

The massive N = 2 supersymmetric Yang–Mills theory is investigated. Its non-renormalizability is revealed starting from the fourth order of the perturbation theory. The N = 2 harmonic superspace approach and the Stueckelberg-like formalism are used. The Stueckelberg fields form some nonlinear sigma model. Non-renormalizability of the latter produces non-renormalizability of the N = 2 supersymmetric Yang–Mills theory.

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A Yang–Mills Theory in Loop Space and Chapline–Manton Coupling

Modern Physics Letters A ◽

10.1142/s0217732397000108 ◽

1997 ◽

Vol 12 (02) ◽

pp. 111-119 ◽

Cited By ~ 2

Author(s):

Shinichi Deguchi ◽

Tadahito Nakajima

Keyword(s):

Field Theory ◽

Local Field ◽

Loop Space ◽

Tensor Field ◽

Symmetric Tensor ◽

Tensor Fields ◽

Yang Mills ◽

Local Field Theory ◽

Antisymmetric Tensor Field ◽

Chern Simons

We consider a Yang–Mills theory in loop space with the affine gauge group. From this theory, we derive a local field theory with Yang–Mills fields and Abelian antisymmetric and symmetric tensor fields of the second rank. The Chapline–Manton coupling, i.e. coupling of Yang–Mills fields and a second-rank antisymmetric tensor field via the Chern–Simons three-form is obtained systematically.

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STOCHASTIC QUANTIZATION AND 1/N EXPANSION

Modern Physics Letters A ◽

10.1142/s0217732393000131 ◽

1993 ◽

Vol 08 (02) ◽

pp. 115-128

Author(s):

J.C. BRUNELLI ◽

R.S. MENDES

Keyword(s):

Perturbation Theory ◽

Sigma Model ◽

Functional Approach ◽

Two Dimensions ◽

Field Theories ◽

Nonlinear Sigma Model ◽

Stochastic Quantization ◽

Quantization Method ◽

Systematic Procedure

We study the 1/N expansion of field theories in the stochastic quantization method of Parisi and Wu using the supersymmetric functional approach. This formulation provides a systematic procedure to implement the 1/N expansion which resembles the ones used in the equilibrium. The 1/N perturbation theory for the nonlinear sigma-model in two dimensions is worked out as an example.

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